A371538 - OEIS

%I #10 Mar 27 2024 08:53:18

%S 1,3,18,151,1440,14835,160793,1806849,20859129,245905348,2947869600,

%T 35825319390,440372147956,5465555197818,68396554601013,

%U 862066323857486,10933638171672105,139439595024315675,1787056241039876890,23003636498360053905,297283046361025602900

%N G.f. A(x) satisfies A(x) = (1 + x*A(x)^2 / (1+x))^3.

%F a(n) = 3 * Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,n-k) * binomial(6*k+3,k)/(6*k+3).

%F G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A349362.

%o (PARI) a(n) = 3*sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(6*k+3, k)/(6*k+3));

%Y Cf. A349362, A371537, A371539, A371540, A371541.

%Y Cf. A371522.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 26 2024